منابع مشابه
Generating the Pfaffian closure with total Pfaffian functions
Given an o-minimal expansion R of the real field, we show that the structure obtained from R by iterating the operation of adding all total Pfaffian functions over R defines the same sets as the Pfaffian closure of R . 2010 Mathematics Subject Classification 14P10,03C64 (primary); 58A17 (secondary)
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We give sign-reversing involution proofs of a pair of two variable Pfaffian identities. Applications to symmetric function theory are given, including identities relating Pfaffians and Schur functions. As a corollary we are able to compute the plethysm p2 ° skn •
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It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of Pfaffians. In this article, we review the formulations and applications of Pfaffian formulas. For that purpose, we first present the general Pfaffian e...
متن کاملComplexity of Computations with Pfaffian and Noetherian Functions
This paper is a survey of the upper bounds on the complexity of basic algebraic and geometric operations with Pfaffian and Noetherian functions, and with sets definable by these functions. Among other results, we consider bounds on Betti numbers of sub-Pfaffian sets, multiplicities of Pfaffian intersections, effective Lojasiewicz inequality for Pfaffian functions, computing frontier and closure...
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The color type of a spanning forest of a graph with colored edges is defined and, subsequently, it is proved that the generating function of such spanning forests is obtained as the formal expansion of a certain determinant. An analogous determinantal expansion yields the generating function of all spanning forests of a given color type that contain a specific subforest. Algorithms are describe...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2015
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-015-0786-6